The wavefunction is the archetype of potential in quantum mechanics. Its meaning, however, is not fixed; it shifts as our understanding of potential evolves. By following the lineage of potential in the relational ontology, we can trace a story of the wavefunction itself — from intuitive readiness to relational, perspectival, and historically evolving possibility.
Phase 1: Readiness — Inclination and Ability
In the earliest construal, the wavefunction is a system poised to realise outcomes. It embodies readiness, with two intertwined aspects: inclination and ability. Inclination captures the system’s tendency to produce certain measurement results, while ability describes the structural competence to realise them.
In this reading, the wavefunction seems to “wait” for measurement. Some outcomes are more ready, more likely to appear, as if the system holds them in a latent store. The intuition is clear: the wavefunction differentiates possibilities and gives a sense of which are easier or more immediate. Yet lurking in this simplicity are temporal and causal metaphors that mislead. Potential seems to reside inside the system, as if it were something waiting to be released.
Phase 2: Latent Structure — Mapping Possibility
The next construal reframes the wavefunction as a space of possibilities, moving away from readiness. The amplitudes no longer describe latent tendencies; they map the relational structure of what could occur.
Now, potential is formal rather than dispositional: the wavefunction charts what is possible under the system’s constraints. It is still a landscape, but one defined by relational rules rather than stored readiness. Novelty is implicit, but the edges of potential are not yet clearly articulated.
Phase 3: System as Theory — Potential is the Wavefunction
A decisive move reframes the wavefunction entirely: it is the system itself. Potential is no longer a property the system “has” but is the system. To specify the wavefunction is to specify all possible instances it admits.
Measurements are contingent events satisfying this system. There is no hidden content, no stored “propensity” waiting to collapse. Novel outcomes emerge relationally, from the structure of the system itself. Here, the wavefunction embodies the shift from dispositional metaphors to a formal, relational, and generative understanding of potential.
Phase 4: Perspective — Potential and Instance as Poles
The wavefunction acquires a new subtlety under the perspectival cut. Viewed from one orientation, it represents pure potential. Viewed from another, a particular measurement outcome is an instance. The shift is not temporal or causal; it is perspectival. There is no collapse-as-process. The wavefunction’s dual character — as relational potential and as realised instance — is revealed as a matter of description, not physics.
Phase 5: Sub-Potentials — Localised Constraints
Within the wavefunction, certain eigenstates or sectors can be seen as sub-potentials. These are locally constrained sets of possibilities. They explain why certain transitions or interactions dominate, without invoking hidden layers. Sub-potentials highlight patterned regularity in relational potential, showing that the system is both structured and selectively constrained.
Phase 6: Horizon — The Edge of Novelty
The wavefunction’s horizon captures what could occur next. Each measurement, interaction, or construal shifts this edge of possibility. Horizons make novelty explicit: they articulate the forward-facing openness of potential without suggesting readiness or latent content. The wavefunction thus retains a relational dynamism: potential is always evolving at the boundary of actualisation, shaped by its ongoing construal.
Phase 7: Evolution — Historical Shaping
Finally, potential itself evolves. The wavefunction’s possibilities are historically conditioned: prior actualisations, stabilisations, and relational constraints influence what remains available. This evolution is non-teleological. The wavefunction, over sequences of interactions, records the relational shaping of potential — its past constrains, its present structures, and its horizon remains open for future novelty.
Rejected Readings
Along the way, several classical or intuitive readings are rejected. The wavefunction is not causal power, latent content, value-laden, pre-meaning substrate, or a classical probability distribution. These readings would violate relational, perspectival, and non-representational commitments. What remains is the wavefunction as a living, relational, evolving system of potential.
Epilogue: Continuity and Transformation
Through this story, the wavefunction mirrors the conceptual evolution of potential itself. From readiness to relational structure, from sub-potentials to horizon and historical evolution, it embodies the shift from intuitive, temporally loaded metaphors to a precise, perspectival, and generative understanding.
The wavefunction is at once familiar and transformed. It remains the archetype of potential, yet its meaning now rests entirely in relationality, perspectival cuts, and evolving possibility — a system alive with constraints, edges, and history, without ever invoking stored readiness or hidden content.
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